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CHAMP’s TRIPLE PASSAGE THROUGH 31 st /62 nd -ORDER ORBIT RESONANCE

CHAMP’s TRIPLE PASSAGE THROUGH 31 st /62 nd -ORDER ORBIT RESONANCE. R.H. Gooding, C.A. Wagner, J. Klo kočník, J. Kostele ck ý.

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CHAMP’s TRIPLE PASSAGE THROUGH 31 st /62 nd -ORDER ORBIT RESONANCE

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  1. CHAMP’s TRIPLE PASSAGE THROUGH 31st/62nd-ORDER ORBIT RESONANCE R.H. Gooding, C.A. Wagner, J. Klokočník, J. Kostelecký

  2. Lagrange planetary equationsthe case of orbital inclination1. Allan/Kaula expression2.after choice of resonant indices3.final resonant form with lumped coefficients1.

  3. Lagrange Planetary Equations with resonant choice for (l,m,p,q)

  4. Lagrange Planetary Equation for Orbital Inclination in terms of Lumped Geopotential Coefficients (LC)

  5. DEFINITIONSResonant angleLumped coefficients

  6. Location of resonances what is semi-major axis / mean motion at exact resonance Two types of semi-major axis: Brouwer Kozai

  7. CHAMP and RESONANCES • CHAMP mission • Location of resonances in CHAMP orbit • simulation of forthcoming resonances in inclination • preparation for analysis of individual resonances • analysis of inclination variations at 46/3 and 31/2 resonances

  8. Comparison of approaches to analyse CHAMP resonances: long-arc vs short-arc • general geopotential recovery from tracking data is to analyse full spectrum of effects in many short-arcs [e.g. 1.5 day for CHAMP] • traditional “resonant analyses” work with long-arc approach and concentrate on few “resonant frequencies” (31/2, 46/3….etc)

  9. Resonance 31/2

  10. Conclusions • Introduction to theory of resonant phenomenon in orbits of Earth artificial satellites • Historical analyses (Gooding etc) • lumped coefficients • rotation of upper atmosphere • calibration of comprehensive solutions for geopotential

  11. CHAMP: • Location, estimation of expected orbit effects and analysis of particular high-order resonances in CHAMP orbit • Comparison of computed lumped geopotential coefficients from resonances with those from comprehensive Earth models • Interpretation of existing discrepancies (due mainly to insufficient modelling of tides and non- gravitational effects in our resonant software), and a possibility to calibrate the Earth models by results from resonances

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